The solution of the given Inequality i.e. -3<2x+3≤5 is x > -3 and x ≤1 (option B).
Inequality:
When the symbols ">", "<", "≤", or "≥" are used to connect two real numbers or algebraic expressions, that relationship is known as an Inequality.
Here the given Inequality is -3<2x+3≤5
⇒ -3<2x+3≤5
⇒-3-3 < 2x+3-3 ≤ 5-3 { add -3 on both the sides }
⇒-6 < 2x ≤ 2
⇒-3 < x ≤ 1
⇒-3 < x and x ≤ 1
⇒ x > -3 and x ≤1
Therefore,The solution of the given Inequality i.e. -3<2x+3≤5 is x > -3 and x ≤1 (option B).
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Answer:
0.00815664062
Step-by-step explanation:
1.33 divide 3.14 times 512 = 0.00815664062
Answer is 0.008 in short form
Hope this helps.
Answer:I'm guessing there's a simpler solution, but let's give it a shot.
Step-by-step explanation:
The two roots are provided by using the quadratic equation:
x = [-b ± √(b2 - 4ac)] / (2a)
For x2 - 10x + q = 0
a = 1
b = -10
c = q
Substituting these values in:
x = [-b ± √(b2 - 4ac)] / (2a)
= [-(-10) ± √((-10)2 - 4(1)(q))] / (2(1))
= [10 ± √(100 - 4q)] / 2
= 0.5 [10 ± √(100 - 4q)]
The first root, x1
x1 = 0.5 [10 + √(100 - 4q)]
= 5 + 0.5√(100 - 4q)
The second root, x2
x2 = 0.5 [10 - √(100 - 4q)]
= 5 - 0.5√(100 - 4q)
The difference in the roots is 6.
6 = x1 - x2
= [5 + 0.5√(100 - 4q)] - [5 - 0.5√(100 - 4q)]
= 5 + 0.5√(100 - 4q) - 5 + 0.5√(100 - 4q)
6 = √(100 - 4q)
(6)2 = [√(100 - 4q)]2
36 = 100 - 4q
-64 = -4q
q = 16
Do a little more work to determine the roots.
x2 - 10x + q = 0
x2 - 10x + 16 = 0
(x - 8)(x - 2) = 0
x = {2, 8}
8 - 2 = 6
Answer:
Jeremiah is correct
Step-by-step explanation:
The absolute value of both shows that Jeremiah got 2 and joseph got 3, on the number line 2 is closer to zero than three. Joseph is incorrect as he is trying to see who got the lower score without converting to the absolute value.
You can use proportional reasoning to answer this question.
Set up a ratio with how far she traveled in the first 2 1/3 mins. Make is equal to x feet in 8 minutes. Solve using cross products.
<u>1r feet </u> <u> x feet</u>
2 1/3 min = 8 mins
<u>8r feet</u> = <u>2 1/3 x</u>
2 1/3 2 1/3
3 3/7r feet = x
In 8 minutes, Maggie descended 3 3/7r feet.